Question

You own a house worth $400,000 on a river. If the river floods moderately, the house will be completely destroyed. This happens about once every 50 years. If you build a seawall, the river would have to flood heavily to destroy your house, and this only happens about once every 200 years. THIS IS THE PROBABILITY: "...once every 50 years," and "once every 200 years." Please answer the questions. Thank you

What are your expected annual costs to the nearest dollar with a seawall and full insurance?                                                                $
What are your expected annual costs to the nearest dollar with a seawall and partial coverage?                                                          $

How much would you be willing to pay annually to the nearest dollar for the cost of building and maintaining a seawall with full insurance?       $
How much would you be willing to pay annually to the nearest dollar for the cost of building and maintaining a seawall with partial coverage?

Answer 1

Assuming that the partial covergae is of 75%

the insurance premium is based on the probability of flooding:

without seawall: 1 every 50 years: 1/50 = 0.02 = 2%

with seawall: 1 every 200 years: 1/200 = 0.005 = 0.5%

With the full insurance the expected annual costs are as follows :

400,000 x 2%    = 8,000 (without a seawall)

400,000 x 0.5% = 2,000 (with a seawall)

With the partial insurance for 75%: the annual costs are expected as follows

400,000 x 75% = 300,000

300,000 x 2% = 6,000 (without a seawall)

300,000 x 0.5% = 1,500(with a seawall)

I will build the seawall if the cost for mainting it are less than the premium difference:

$8,000 - $2,000 = $6,000 per year

If the seawall cost less than this amount is better to build it.